
The mixing among the two \(U(1)\)  factor occur in the kinetic and also in the mass terms. In this case the photon has a component on \(Z^\prime \) . See, for instance, the model of Babu et al., in Ref. [1]}.

The mixing among the two \(U(1)\)  factors occurs only in the kinetic term. Examples of these sort of model are our model and that of Ref. [2]}. In these models the photon has no component on \(Z^ \prime \) .

